Find points at a given distance on a line of given slope

Given the co-ordinates of a 2-dimensional point p(x₀, y₀). Find the points at a distance L away from it, such that the line formed by joining these points has a slope of M.

Examples: 

Input : p = (2, 1)
        L = sqrt(2)
        M = 1
Output :3, 2
        1, 0
Explanation:
The two points are sqrt(2) distance away 
from the source and have the required slope
m = 1.

Input : p = (1, 0)
        L = 5
        M = 0
Output : 6, 0
        -4, 0

We need to find two points that are L distance from given point, on a line with slope M.
The idea has been introduced in below post. 
Find Corners of Rectangle using mid points

Based on the input slope, the problem can be classified into 3 categories.  

1. If slope is zero, we just need to adjust the x coordinate of the source point
2. If slope is infinite, the we need to adjust the y coordinate
3. For other values of slope, we can use the following equations to find the points

Now using the above formula we can find the required points.

C++

// C++ program to find the points on a line of
// slope M at distance L
#include <bits/stdc++.h>
using namespace std;

// structure to represent a co-ordinate
// point
struct Point {

    float x, y;
    Point()
    {
        x = y = 0;
    }
    Point(float a, float b)
    {
        x = a, y = b;
    }
};

// Function to print pair of points at
// distance 'l' and having a slope 'm'
// from the source
void printPoints(Point source, float l,
                                 int m)
{
    // m is the slope of line, and the
    // required Point lies distance l
    // away from the source Point
    Point a, b;

    // slope is 0
    if (m == 0) {
        a.x = source.x + l;
        a.y = source.y;

        b.x = source.x - l;
        b.y = source.y;
    }

    // if slope is infinite
    else if (m == std::numeric_limits<float>
                                 ::max()) {
        a.x = source.x;
        a.y = source.y + l;

        b.x = source.x;
        b.y = source.y - l;
    }
    else {
        float dx = (l / sqrt(1 + (m * m)));
        float dy = m * dx;
        a.x = source.x + dx;
        a.y = source.y + dy;
        b.x = source.x - dx;
        b.y = source.y - dy;
    }

    // print the first Point
    cout << a.x << ", " << a.y << endl;

    // print the second Point
    cout << b.x << ", " << b.y << endl;
}

// driver function
int main()
{
    Point p(2, 1), q(1, 0);
    printPoints(p, sqrt(2), 1);
    cout << endl;
    printPoints(q, 5, 0);
    return 0;
}

Java

// Java program to find the points on
// a line of slope M at distance L
class GFG{

// Class to represent a co-ordinate
// point
static class Point
{
    float x, y;
    Point()
    {
        x = y = 0;
    }
    Point(float a, float b)
    {
        x = a;
        y = b;
    }
};

// Function to print pair of points at
// distance 'l' and having a slope 'm'
// from the source
static void printPoints(Point source,
                        float l, int m)
{

    // m is the slope of line, and the
    // required Point lies distance l
    // away from the source Point
    Point a = new Point();
    Point b = new Point();

    // Slope is 0
    if (m == 0)
    {
        a.x = source.x + l;
        a.y = source.y;

        b.x = source.x - l;
        b.y = source.y;
    }

    // If slope is infinite
    else if (Double.isInfinite(m))
    {
        a.x = source.x;
        a.y = source.y + l;

        b.x = source.x;
        b.y = source.y - l;
    }
    else
    {
        float dx = (float)(l / Math.sqrt(1 + (m * m)));
        float dy = m * dx;
        a.x = source.x + dx;
        a.y = source.y + dy;
        b.x = source.x - dx;
        b.y = source.y - dy;
    }

    // Print the first Point
    System.out.println(a.x + ", " + a.y);

    // Print the second Point
    System.out.println(b.x + ", " + b.y);
}

// Driver code
public static void main(String[] args)
{
    Point p = new Point(2, 1),
          q = new Point(1, 0);
    printPoints(p, (float)Math.sqrt(2), 1);

    System.out.println();

    printPoints(q, 5, 0);
}
}

// This code is contributed by Rajnis09

C#

// C# program to find the points on
// a line of slope M at distance L
using System;

class GFG{

// Class to represent a co-ordinate
// point
public class Point
{
    public float x, y;

    public Point()
    {
        x = y = 0;
    }

    public Point(float a, float b)
    {
        x = a;
        y = b;
    }
};

// Function to print pair of points at
// distance 'l' and having a slope 'm'
// from the source
static void printPoints(Point source,
                        float l, int m)
{

    // m is the slope of line, and the
    // required Point lies distance l
    // away from the source Point
    Point a = new Point();
    Point b = new Point();

    // Slope is 0
    if (m == 0)
    {
        a.x = source.x + l;
        a.y = source.y;

        b.x = source.x - l;
        b.y = source.y;
    }

    // If slope is infinite
    else if (Double.IsInfinity(m))
    {
        a.x = source.x;
        a.y = source.y + l;

        b.x = source.x;
        b.y = source.y - l;
    }
    else
    {
        float dx = (float)(l / Math.Sqrt(
                           1 + (m * m)));
        float dy = m * dx;
        a.x = source.x + dx;
        a.y = source.y + dy;
        b.x = source.x - dx;
        b.y = source.y - dy;
    }

    // Print the first Point
    Console.WriteLine(a.x + ", " + a.y);

    // Print the second Point
    Console.WriteLine(b.x + ", " + b.y);
}

// Driver code
public static void Main(String[] args)
{
    Point p = new Point(2, 1),
          q = new Point(1, 0);

    printPoints(p, (float)Math.Sqrt(2), 1);

    Console.WriteLine();

    printPoints(q, 5, 0);
}
}

// This code is contributed by Amit Katiyar

Output: 

3, 2
1, 0

6, 0
-4, 0

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